docs(ui): drop sidebar saved-state — server defaults already ARE the standard docs behavior

Simplification per spec: the menu tracks state through the URL alone.
Land on /docs: fully closed, headers only (an explicit home rule now
overrides the contains-URL rule, since the root overview doc lives in
Getting Started and would otherwise auto-open it). Land on any doc page:
its containing section + group render open at first paint, current link
bold — no JS, no jump, arrows consistent. Navigate elsewhere: old
closes, new opens.

Deleted: docs_nav cookie const/parse, ApplyNavOverrides, cookie write +
collect/persist helpers in web/src/docs.ts, data-key attributes in the
sidebar templ, and the first-section-open fallback (docs home used to
force-open the first section — spec'd as closed).

toggleCollapsible remains for in-page peeking; purely ephemeral.
The [data-collapsed=true] CSS from the previous round stays — it is what
makes the server-rendered state actually hide sections at paint (the
original bug was that this CSS never existed).

Tests: TestBuildNavigationNothingCurrent now asserts zero sections open
on unmatched paths; TestBuildNavigation asserts Getting Started closed
on a device page (no site-wide pin). make test green; 146 vitests; live
verified: home 0 expanded, doc pages exactly 2 (section+group).

internal/docs/navigation.go

@@ -178,8 +178,8 @@ func docURL(docPath string) string {
 
 // BuildNavigation creates the category → subcategory navigation from the
 // docs filesystem. The section and group containing currentPath render
-// expanded; everything else starts collapsed (with Getting Started as the
-// fallback when nothing matches).
+// expanded; everything else starts collapsed. When nothing matches (docs
+// home, 404), the sidebar renders fully closed — headers only.
 func (h *DocsHandler) BuildNavigation(currentPath string) *templates.Navigation {
 	docs, err := h.ListDocuments()
 	if err != nil {
@@ -198,16 +198,17 @@ func (h *DocsHandler) BuildNavigation(currentPath string) *templates.Navigation
 	}
 
 	type groupBuild struct {
-		items    []templates.NavItem
-		urls     []string
-		overview bool // has a pinned index page
+		items []templates.NavItem
+		urls  []string
+		// overview: the group leads with its "#"Overview landing doc (pinned
+		// subdirectory index), so it sorts first.
+		overview bool
 	}
 	type sectionBuild struct {
-		items    []templates.NavItem
-		urls     []string
-		pinned   map[string]bool // landing pages lead their section
-		groups   map[string]*groupBuild
-		overview bool
+		items  []templates.NavItem
+		urls   []string
+		pinned map[string]bool // landing pages lead their section
+		groups map[string]*groupBuild
 	}
 
 	builds := make(map[string]*sectionBuild, len(sectionOrder))
@@ -231,10 +232,6 @@ func (h *DocsHandler) BuildNavigation(currentPath string) *templates.Navigation
 			if place.pin < 0 {
 				build.pinned[item.URL] = true
 			}
-			if place.pin == -100 {
-				// Only the root Overview forces its section open.
-				build.overview = true
-			}
 		} else {
 			group, ok := build.groups[place.group]
 			if !ok {
@@ -301,52 +298,24 @@ func (h *DocsHandler) BuildNavigation(currentPath string) *templates.Navigation
 				}
 			}
 		}
-		if build.overview {
-			section.Collapsed = false
-		}
 		nav.Sections = append(nav.Sections, section)
 	}
 
-	// Nothing matches the current page (404, search landing): open the
-	// first section so the sidebar doesn't render fully closed.
-	anyOpen := false
-	for _, s := range nav.Sections {
-		if !s.Collapsed {
-			anyOpen = true
-			break
+	// No default expansion when nothing matches the current page (404,
+	// search landing): the sidebar renders fully closed. Same for the docs
+	// HOME: although the root overview doc lives there (its contains-URL
+	// rule would open "Getting Started"), the spec is "home = all closed,
+	// headers only" — the standard docs-site behavior.
+	if strings.TrimSuffix(currentPath, "/") == "/docs" {
+		for si := range nav.Sections {
+			nav.Sections[si].Collapsed = true
 		}
-	}
-	if !anyOpen && len(nav.Sections) > 0 {
-		nav.Sections[0].Collapsed = false
+		return nav
 	}
 
 	return nav
 }
 
-// ApplyNavOverrides merges the browser-saved collapse state (docs_nav
-// cookie) into the nav so the sidebar first-paints in the visitor's chosen
-// state — no post-paint JS correction, no jumping. Keys mirror the
-// data-key attributes DocsSidebar renders: section titles, and
-// "Section / Group" for groups. Entries for unknown keys (renamed or
-// removed sections) are ignored; keys absent from the map keep the
-// path-derived default.
-func ApplyNavOverrides(nav *templates.Navigation, overrides map[string]bool) {
-	if len(overrides) == 0 {
-		return
-	}
-	for si := range nav.Sections {
-		s := &nav.Sections[si]
-		if v, ok := overrides[s.Title]; ok {
-			s.Collapsed = v
-		}
-		for gi := range s.Groups {
-			if v, ok := overrides[s.Title+" / "+s.Groups[gi].Title]; ok {
-				s.Groups[gi].Collapsed = v
-			}
-		}
-	}
-}
-
 // containsURL reports whether currentPath is one of the given doc URLs.
 func containsURL(currentPath string, urls []string) bool {
 	for _, u := range urls {